What is the optimal time complexity of solving Heap Sort?

The optimized solution achieves a time complexity of O(n log n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Heap Sort?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Heap Sort?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Heap Sort?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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DSA SectionEasy

Heap Sort

Learn how to solve the 'Heap Sort' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function heap_sort(arr) that sorts a list of integers arr in ascending order using the Heap Sort algorithm (building a max heap first) and returns the sorted list.

Constraints

•0 <= len(arr) <= 10^4
•-10^5 <= arr[i] <= 10^5

Examples

Example 1

Input

arr = [12, 11, 13, 5, 6, 7]

Output

[5, 6, 7, 11, 12, 13]

Explanation

A max heap is created, the maximum element is repeatedly swapped with the last element of the heap, and heapify is performed.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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